Robust median estimator for generalized linear models with binary responses

Tomáš Hobza; Leandro Pardo; Igor Vajda

Kybernetika (2012)

  • Volume: 48, Issue: 4, page 768-794
  • ISSN: 0023-5954

Abstract

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The paper investigates generalized linear models (GLM's) with binary responses such as the logistic, probit, log-log, complementary log-log, scobit and power logit models. It introduces a median estimator of the underlying structural parameters of these models based on statistically smoothed binary responses. Consistency and asymptotic normality of this estimator are proved. Examples of derivation of the asymptotic covariance matrix under the above mentioned models are presented. Finally some comments concerning a method called enhancement and robustness of median estimator are given and results of simulation experiment comparing behavior of median estimator with other robust estimators for GLM's known from the literature are reported.

How to cite

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Hobza, Tomáš, Pardo, Leandro, and Vajda, Igor. "Robust median estimator for generalized linear models with binary responses." Kybernetika 48.4 (2012): 768-794. <http://eudml.org/doc/246708>.

@article{Hobza2012,
abstract = {The paper investigates generalized linear models (GLM's) with binary responses such as the logistic, probit, log-log, complementary log-log, scobit and power logit models. It introduces a median estimator of the underlying structural parameters of these models based on statistically smoothed binary responses. Consistency and asymptotic normality of this estimator are proved. Examples of derivation of the asymptotic covariance matrix under the above mentioned models are presented. Finally some comments concerning a method called enhancement and robustness of median estimator are given and results of simulation experiment comparing behavior of median estimator with other robust estimators for GLM's known from the literature are reported.},
author = {Hobza, Tomáš, Pardo, Leandro, Vajda, Igor},
journal = {Kybernetika},
keywords = {generalized linear models; binary responses; statistical smoothing; statistical enhancing; maximum likelihood estimator; median estimator; consistency; asymptotic normality; efficiency; robustness; generalized linear models; binary responses; statistical smoothing; statistical enhancing; maximum likelihood estimator; median estimator; consistency; asymptotic normality; efficiency; robustness},
language = {eng},
number = {4},
pages = {768-794},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Robust median estimator for generalized linear models with binary responses},
url = {http://eudml.org/doc/246708},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Hobza, Tomáš
AU - Pardo, Leandro
AU - Vajda, Igor
TI - Robust median estimator for generalized linear models with binary responses
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 4
SP - 768
EP - 794
AB - The paper investigates generalized linear models (GLM's) with binary responses such as the logistic, probit, log-log, complementary log-log, scobit and power logit models. It introduces a median estimator of the underlying structural parameters of these models based on statistically smoothed binary responses. Consistency and asymptotic normality of this estimator are proved. Examples of derivation of the asymptotic covariance matrix under the above mentioned models are presented. Finally some comments concerning a method called enhancement and robustness of median estimator are given and results of simulation experiment comparing behavior of median estimator with other robust estimators for GLM's known from the literature are reported.
LA - eng
KW - generalized linear models; binary responses; statistical smoothing; statistical enhancing; maximum likelihood estimator; median estimator; consistency; asymptotic normality; efficiency; robustness; generalized linear models; binary responses; statistical smoothing; statistical enhancing; maximum likelihood estimator; median estimator; consistency; asymptotic normality; efficiency; robustness
UR - http://eudml.org/doc/246708
ER -

References

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